Emergent mechanics of endocytic protein assembly

Max Ferrin

PhD candidate, Drubin/Barnes Lab

Clathrin-mediated endocytosis (CME)

(Lacy et al., 2018)

the cellular system I studied in my PhD is called clathrin mediated endocytosis (abbreviated to CME), which is the primary pathway for internalization of extracellular and membrane cargo in eukaryotic cells
what this looks like morphologically is diagrammed in this cartoon, which is a cross-section through a eukaryotic cell's plasma membrane
a small patch of plasma membrane and associated cargo is pulled into the cytoplasm and pinched off to result in an endocytic vesicle
concurrent with this is the sequential recruitment of endocytic proteins, which following an initial variable period, all appear with very very predictable timing to assist in the generation of the endocytic vesicle
while members of the lab study many aspects of CME from structure and biochemistry to physiology, my own research has focused on the mechanical forces at play

CME is mechanically complex

(Lacy et al., 2018)

Thesis outline: What emergent mechanics arise from interactions among endocytic components?

in my dissertation, I plan to write up my work I contributing to the following areas of endocytic mechanics:
- first is my analytical contributions to the published paper on actin self-organization for load adaptation (theory)
- then my brief unpublished work attempting to follow up on the previous project by studying type I myosin's actin-binding kinetics (theory)
- then my co-first authored manuscript on actin network-mediated protein recruitment and membrane budding that we are days to weeks from submitting (experiment)
- and finally my current work in progress, mechanical influence of liquid-like biomolecular condensate (theory and experiment)
the first two are things that weren't a huge part of my thesis, but I do want to write up my contributions to them so I'll speed through them very quickly
I also want to speed through third thing because it's complete
I want to spend most of the time talking about my highest priority for finishing
I just want to focus on what is done and what is left to do
maybe highlight the diversity of techniques I mastered here as well
- live cell microscopy
- defined in vitro reactions
- hybrid reconstitution
- theoretical modeling

Chapter 1: Actin self-organization for load adaptation during CME

How is the force-generating endocytic actin network able to reorganize in response to increasing opposing force?

(Akamatsu et al., 2020)

Motivation: Size and shape of endocytic actin network changes as membrane tension increases

(Kaplan et al., 2022)

Theoretical approach: Agent-based model of minimal actin network in CME

(Nedelec and Foethke, 2007; Akamatsu et al., 2020)

Qualitative recapitulation of increased actin density in response to increased membrane tension

Analysis of simulations reveals quantitative measurements of actin self-organization

Manipulation of actin-coat linkers abolishes adaptive response to tension by disrupting self-organization

Model of load-responsive actin network self-organization

(Akamatsu et al., 2020)

Chapter 2: Type I myosin's actin-binding kinetics

Does the potential catch-bond activity of myosin serve an emergent function in CME?

Motivation: Diversity of myosin force sensitivity

(Laakso et al., 2008; Pedersen, 2019)

Theoretical approach: Minimal model of CME with myosins

Generating a model non-processive motor

Coarsely tuning force sensitivity to similar myosin measurements

(Greenberg et al., 2012)

Systematic quantitative analysis of CME simulations

Simulations predict optimal range of actin-binding kinetics for CME robustness

Strong catch bonds hold actin in non-productive orientation

Weak catch bonds appear to exert force through actin network

Weak catch bond myosins qualitatively recapitulate internalization velocity measurements

(Manenschijn et al., 2019)

Summary: Weak myosin catch bonds aid CME robustness

Chapter 3: Actin network-mediated protein recruitment and membrane budding

How much of mechanically productive actin network architecture is encoded by its building blocks?

Experimental reconstitution approach: mix purified protein-coated SLBs with yeast cytoplasmic extract

Recapitulation of sequential endocytic protein assembly

Reconstitution of actin-mediated vesicle budding

Summary: CME actin network can self-organize for endocytosis-like force production

Chapter 4: Mechanical influence of liquid-like biomolecular condensate

Are capillary forces of a liquid condensate assistive or resistant to endocytic membrane bending?

Motivation: Mounting evidence of CME proteins forming liquid-like condensates

(Li et al., 2012; Bergeron-Sandoval et al., 2021; Day et al., 2021; Kozak and Kaksonen, 2022)

Motivation: Condensates can deform membranes through capillary forces

(Kusumaatmaja et al., 2021)

from examples in other systems, we know these capillary forces can be strong enough to deform membranes
there are several examples of a variety of protein condensate and membrane system that look like this: the wetting and surface tension drive the membrane to wrap around the condensate
similar interfaces exist in an endocytic protein condensate
however due to additional mechanical constraints directing membrane bending into the cytoplasm such as the cell wall and directional curvature-generating proteins, it's actually non-trivial to predict how the condensate capillary forces will affect the mechanics of membrane bending when it has to bend into the condensate

by definition, when a solution phase-separates, new interfaces are created between the condensed phase and dilute phase, as well as with a surface if that's present
these interfaces experience interfacial forces, which are commonly referred to as capillary forces
in liquid-like condensates and membranes, the relevant capillary forces are surface tension of the condensed-dilute phase interface and wetting at the condensed phase-membrane interface
- these are higher-order emergent properties arising from building block interactions: condensed phase proteins have more energetically favorable interactions with themselves and with the membrane than with the solute in the dilute phase
in this particular example of storage vacuoles of arabidopsis embryos, we see that these forces lead to deformation of the vacuolar membrane

Capillary forces are present in CME

Mathematical model of CME mechanical energy

so in order to gain that predictive understanding of these forces in isolation, I took a theoretical modeling approach to model the mechanical energy of a condensate during endocytosis
on the left is a 3d visualization of the model I built which consists of a membrane invagination in blue that can transition from flat to spherical, and a liquid protein condensate in green surrounding it
there's only 1 variable to keep track of in this talk which is h, the relative invagination distance from 0 (flat) to 1 (spherical)
based on the geometry at every point of h, I can calculate the change in free energy of individual components:
- positive free energy is unfavorable, negative is favorable
- surface tension of condensate-cytosol interface
- wetting energy of condensate-membrane interface
- membrane tension from pulling in membrane
- bending energy from spontaneous curvature of protein-coated invagination
- turgor pressure from volume of invagination
- all of these get added up into the sum for the whole system
in this particular set of parameters, endocytosis is energetically favorable

Condensate can provide net assistive force through wetting

Condensate surface tension results in energy barrier to initiation of membrane bending

The condensate can never be assistive to the flat-curved membrane transition

Droplet volume sets the energy barrier amplitude and position

Droplet volume sets the energy barrier amplitude and position

Summary: Condensate capillary forces inhibit membrane bending initiation, but assist completion

so in putting it all together, I have revealed a few forces that arise from condensate-membrane interactions
a condensate resists bending of a flat membrane into the condensate, but that force becomes weaker as the condensate volume increases
after bending is initiated, the system passes the energy barrier and the condensate can drive toward a net decrease in free energy
this leads to a potential physiological function of a condensate early in CME:
a condensate could slow things down during initiation while the machinery and cargo are accumulating, but drive toward complete invagination after a certain threshold
this is consistent with what we know about CME initiation being highly variable, followed by very reliable timing of internalization
this is the minimal story I have so far, but I have been putting in a lot of work to make it more complete

Manuscript figure outline

Description of biological system and modeling approaches
Qualitative features of toy model
Validation of toy model results with continuum mechanics model
Physiological significance of condensate mechanics by comparing model results to experimentally measured parameters

Fig. 1 panel sketches: Two complementary modeling approaches

Toy geometrical model	Continuum membrane mechanics model

everything is a spherical cap	discretized shapes governed by local forces
can be solved analytically	must be simulated numerically
relatively easy to write out and program	complicated math and simulation techniques required
unrealistic membrane shapes and kinks	realistic membrane curvature
purely equilibrium solution	can simulate temporal dynamics

Fig. 2: Qualitative features of toy model

Fig. 2 Supplement: Different behavior in constant coat area vs. constant curvature alternative models

Fig. 2 Supplement: Free energy landscape of constant coat area vs. constant curvature alternative models

Fig. 3: Does model with realistic membrane bending recapitulate results of toy model?

Fig. 3 supplement: coated membrane stabilizes at predicted curvature

Fig. 3 supplement: condensate stabilizes at predicted contact angle

Fig. 3 results in progress: complementary simulations to toy model

Model condensate stalls initiation of membrane bending at similar parameter regimes between models

Fig. 4: what do condensate mechanics mean for CME function?

under which parameter regimes is there a large vs. negligible effect from the condensate?
which regime do experimental measurements place an endocytic condensate?
what parameters of the model might change over time in situ that could serve as regulatory features?

Fig. 4 panel: example analysis of condensate impact

Hypothetical fig. 4 panels: experimental estimation of condensate model parameters

(Brangwynne et al., 2009; Kozak and Kaksonen, 2022)

Hypothetical fig. 4 panel: regulatory potential of condensate mechanics

Potential thesis timelines

if May 2023 filing date:
- pause theory work
- start writing thesis now
- try to preempt reviewer-requested experiments for reconstitution manuscript
- very quick attempt at minimal condensate fusion and FRAP experiments
- finish condensate theoretical modeling project at Max Planck Institute in Dresden
if August 2023 filing date:
- more buffer time for manuscript reviews
- more time for optimizing condensate experimental system and data collection with summer undergraduate assistance
- write my thesis over the summer
- finish theoretical modeling in Dresden

Thank you!

References

Akamatsu, M. et al. (2020) “Principles of self-organization and load adaptation by the actin cytoskeleton during clathrin-mediated endocytosis,” Elife. Edited by P. Bassereau et al., 9, p. e49840. Available at: https://doi.org/10.7554/eLife.49840.

Bergeron-Sandoval, L.-P. et al. (2021) “Endocytic proteins with prion-like domains form viscoelastic condensates that enable membrane remodeling,” Proceedings of the national academy of sciences, 118(50). Available at: https://doi.org/10.1073/pnas.2113789118.

Brangwynne, C.P. et al. (2009) “Germline P Granules Are Liquid Droplets That Localize by Controlled Dissolution/Condensation,” Science, 324(5935), pp. 1729–1732. Available at: https://doi.org/10.1126/science.1172046.

Day, K.J. et al. (2021) “Liquid-like protein interactions catalyse assembly of endocytic vesicles,” Nature cell biology, 23(4), pp. 366–376. Available at: https://doi.org/10.1038/s41556-021-00646-5.

Greenberg, M.J. et al. (2012) “Myosin IC generates power over a range of loads via a new tension-sensing mechanism,” Proceedings of the national academy of sciences, 109(37), pp. E2433–E2440. Available at: https://doi.org/10.1073/pnas.1207811109.

Kaplan, C. et al. (2022) “Load adaptation by endocytic actin networks,” Molecular biology of the cell, 33(6), p. ar50. Available at: https://doi.org/10.1091/mbc.E21-11-0589.

Kozak, M. and Kaksonen, M. (2022) “Condensation of Ede1 promotes the initiation of endocytosis,” Elife. Edited by M.I. Geli, 11, p. e72865. Available at: https://doi.org/10.7554/eLife.72865.

Kusumaatmaja, H. et al. (2021) “Wetting of phase-separated droplets on plant vacuole membranes leads to a competition between tonoplast budding and nanotube formation,” Proceedings of the national academy of sciences, 118(36), p. e2024109118. Available at: https://doi.org/10.1073/pnas.2024109118.

Laakso, J.M. et al. (2008) “Myosin I can act as a molecular force sensor.,” Science (new york, n.y.), 321(5885), pp. 133–136. Available at: https://doi.org/10.1126/science.1159419.

Lacy, M.M. et al. (2018) “Molecular mechanisms of force production in clathrin-mediated endocytosis,” Febs letters, 592(21), pp. 3586–3605. Available at: https://doi.org/10.1002/1873-3468.13192.

Li, P. et al. (2012) “Phase transitions in the assembly of multivalent signalling proteins,” Nature, 483(7389), pp. 336–340. Available at: https://doi.org/10.1038/nature10879.

Manenschijn, H.E. et al. (2019) “Type-I myosins promote actin polymerization to drive membrane bending in endocytosis,” Elife. Edited by C.G. Burd, A. Akhmanova, and C.G. Burd, 8, p. e44215. Available at: https://doi.org/10.7554/eLife.44215.

Nedelec, F. and Foethke, D. (2007) “Collective Langevin dynamics of flexible cytoskeletal fibers,” New journal of physics, 9(11), p. 427. Available at: https://doi.org/10.1088/1367-2630/9/11/427.

Pedersen, R.T.A. (2019) Cooperative Force Generation by Actin Assembly and Myosin-I During Endocytosis, Proquest dissertations and theses. University of California, Berkeley.